对称性和耗散性在生物运动中的作用
The role of symmetry and dissipation in biolocomotion
摘要：
本文阐述了相对极限环在生物运动中可能起的作用。我们这样做，非常详细地描述，减少一个轻微耗散系统建模爬行式运动在3D的一个基本的例子。对称群SE（2）是水平（地）平面的刚性变换的集合。给定一个时间周期的扰动，系统将允许一个相对的极限环，因此每个周期与前一个周期通过固定的平移和沿地面的旋转而相关。这个玩具模型确定了对称性减少和耗散如何共同创造爬行，可能还有步行，运动的鲁棒行为。
英文摘要：
In this paper we illustrate the potential role which relative limit cycles may play in biolocomotion. We do this by describing, in great detail, an elementary example of reduction of a lightly dissipative system modeling crawling-type locomotion in 3D. The symmetry group SE(2) is the set of rigid transformations of the horizontal (ground) plane. Given a time-periodic perturbation, the system will admit a relative limit cycle whereupon each period is related to the previous by a fixed translation and rotation along the ground. This toy model identifies how symmetry reduction and dissipation can conspire to create robust behavior in crawling, and possibly walking, locomotion.
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